A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement
Annales de l'I.H.P. Probabilités et statistiques (1994)
- Volume: 30, Issue: 2, page 197-211
- ISSN: 0246-0203
Access Full Article
topHow to cite
topDe la Peña, Victor H.. "A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement." Annales de l'I.H.P. Probabilités et statistiques 30.2 (1994): 197-211. <http://eudml.org/doc/77479>.
@article{DelaPeña1994,
author = {De la Peña, Victor H.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {moment generating function; Laplace transform; sampling without replacement; martingales; conditionally independent sequence; conditionally independent sampling},
language = {eng},
number = {2},
pages = {197-211},
publisher = {Gauthier-Villars},
title = {A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement},
url = {http://eudml.org/doc/77479},
volume = {30},
year = {1994},
}
TY - JOUR
AU - De la Peña, Victor H.
TI - A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 2
SP - 197
EP - 211
LA - eng
KW - moment generating function; Laplace transform; sampling without replacement; martingales; conditionally independent sequence; conditionally independent sampling
UR - http://eudml.org/doc/77479
ER -
References
top- [1] M. Arcones and E. Giné, Limit Theorems for U-processes, 1990, To appear in Ann. of Probab. Zbl0789.60031MR1235426
- [2] D.L. Burkholder, A Geometric Condition that Implies the Existence of Certain Singular Integrals of Banach-Space-Valued Functions, Conference on Harmonic Analysis in Honor of Antoni Zygmund, Chicago, 1981, edited by William Beckner, Alberto P. Calderón, Robert Fefferman and Peter W. Jones, Wadsworth, Belmont, California, 1983. MR730072
- [3] Y.S. Chow and H. Teicher, Probability Theory, Springer-Verlag, New York, 1978. Zbl0399.60001MR513230
- [4] V. H. de la Peña, Bounds on the Expectation of Functions of Martingales and Sums of Positive rv's in Terms of Norms of Sums of Independent Random Variables, Proccedings Amer. Math. Soc., Vol. 108, No. 1, pp. 233-239. Zbl0682.60032MR990432
- [5] V. H. de la Peña, Decoupling and Khintchine's Inequalities for U-Statistics, Ann. Probab., Vol. 20, No. 4, 1992, pp. 1877-1892. Zbl0761.60014MR1188046
- [6] V. H. de la Peña, Inequalities for Tails of Adapted Processes with an Application to Wald's Lemma, Journal of Theoretical Probability, Vol. 6, No. 2, 1993. Zbl0780.60018
- [7] P. Hitczenko, Comparison of Moments of Tangent Sequences of Random Variables, Prob. Th. Rel. Fields, Vol. 78, No., 2, 1988, pp. 223-230. Zbl0631.60003MR945110
- [8] P. Hitczenko, Best Constants in Martingale Version of Rosenthal's Inequality, Ann. of Probab., Vol. 18, No. 4, 1990, pp. 1656-1668. Zbl0725.60018MR1071816
- [9] P. Hitczenko, Personal communication, 1991.
- [10] W. Hoeffding, Probability Inequalities for Sums of Bounded Random Variables, Journal of the American Statistical Association, Vol. 58, 1963, pp. 13-30. Zbl0127.10602MR144363
- [11] J. Jacod, Une généralisation des semimartingales : Les processus admettant un processus à accroissements independants tangent, Lecture Notes in Math, No. 1247, 1984, pp. 479-514. Zbl0539.60033MR770952
- [12] A. Jakubowski, Principle of Conditioning in Limit Theorems for Sums of Random Variables, Ann. Probab., Vol. 14, No 3, pp. 902-915. Zbl0593.60031MR841592
- [13] O. Kallenberg and J. Szulga, Multiple Integration with Respect to Poisson and Lévy Processes, Probab. Th. Rel. Fields, Vol. 83, 1989, pp. 101-134. Zbl0681.60049MR1012497
- [14] M.J. Klass, A Best Improvement of Wald's Lemma, Ann. of Probab., Vol. 16, No. 2, 1988, pp. 840-853. Zbl0648.60050MR929081
- [15] M.J. Klass, Uniform Lower Bounds for Randomly Stopped Banach Space-Valued Random Sums, Ann. of Probab., Vol. 18, No. 2, 1990, pp. 790-809. Zbl0706.60046MR1055433
- [16] W. Krakowiak and J. Szulga, On a p-Stable Multiple Integral, II, Probab. Th. Rel. Fields, Vol. 78., No. 3, 1988, pp. 449-453. Zbl0628.60066MR949183
- [17] S. Kwapień, Decoupling Inequalities for Polynomial Chaos,Ann. of Probab., Vol. 15, 1987, pp. 1062-1072. Zbl0622.60026MR893914
- [18] S. Kwapień and W.A. Woyczyński, Semimartingale Integrals via Decoupling Inequalities and Tangent processes, Preprint No. 88-93, Department of Mathematics and Statistics, Case Western Reserve University, 1988. Zbl0778.60041MR1199772
- [19] S. Kwapień and W.A. Woyczyński, Tangent Sequences of Random Variables: Basic Inequalities and their Applications, Proceedings of Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, pp. 237-265, Columbus Ohio, June 1988. G. A. Edgar and L. Sucheston, Editors, Academic Press, New York, 1989. Zbl0693.60033MR1035249
- [20] S. Kwapień and W.A. Woyczyński, Random Series and Stochastic Integrals. Single and Multiple, Birkhäuser, Boston, 1992. Zbl0751.60035MR1167198
- [21] T.R. Mcconnell, and M. Taqqu, Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables, Ann. of Probab., Vol. 14, No. 3, 1986, pp. 943-954. Zbl0602.60025MR841595
- [22] T.R. Mcconnell and M. Taqqu, Decoupling Inequalities for Banach-Valued Multilinear Forms in Independent Symmetric Banach-Valued Random Variables, Probab. Th. Rel. Fields, Vol. 75, 1987, pp. 499-507. Zbl0609.60025MR894902
- [23] T.R. Mcconnell, Decoupling and Stochastic Integration in UMD Banach Spaces, Prob. and Math. Stat., Vol. 10, No. 2, 1989, pp. 283-295. Zbl0718.60050MR1057936
- [24] J. Zinn, Comparison of Martingale Difference Sequences. Proceedings of Conference Probability in Banach Spaces V, Lecture Notes in Mathematics, No. 1153, 1975, pp. 453-457, Springer-Verlag, Berlin. Zbl0571.60058MR821997
Citations in EuDML Documents
top- Victor H. de La Peña, Erratum / Correction to : “A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement”
- Yu Miao, Concentration inequalities for semi-bounded martingales
- Yu Miao, Concentration inequalities for semi-bounded martingales
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.